(August 7, 2012 at 12:01 pm)jonb Wrote:(August 7, 2012 at 8:50 am)CliveStaples Wrote: "every system I will bring up will be assumed to use standard logic for its rules of inference."
By whom?
By me, when I draw inferences. Like if I say, "Oh, p and p->q are true; therefore, q holds", I'm using modus ponens. Or I might use substitution (if P(x) is a predicate statement about x, and x = y, then P(x) <=> P(y)).
The only reason I bother to specify which rules of inference I'm using is to make explicit what reasoning my conclusions are based on, and what it means for something to 'follow from' a previous statement. In general, there are many different rules of inference that could be employed; the standard transformation and substitution rules of propositional/predicate logic are pretty familiar to most people, and I think they're useful for my purpose here.
“The truth of our faith becomes a matter of ridicule among the infidels if any Catholic, not gifted with the necessary scientific learning, presents as dogma what scientific scrutiny shows to be false.”
